ML2 - Time Series
Luisa Yanez y Miguel García
25/07/2022
ML2 - Series Temporales
1. Introducción
La práctica a desarrollar consiste en la elaboración y presentación de un informe de un proyecto de Ciencia de Datos, utilizando las técnicas aprendidas durante la asignatura, aplicadas al conjunto de datos seleccionados.
1.1. Lenguaje de programación y herramienta de control de versiones utilizado
El grupo eligió trabajar en lenguage R (RStudio version 1.4.1717) y utilizar como herramienta de control de versiones GitHub. El proyecto “/ml2_series temporales” fue creado por Luisa Yánez (usuario “lyanezgu”) y compartido con el otro integrante del grupo, Miguel García (usuario “mgarciasanc2021”).
Link del proyecto en GitHub: https://github.com/lyanezgu/ml2_series_temporales
1.2. Paquetes de R
library(readr)
library(tidyverse)
library(tsibble)
library(fable)
library(feasts)
library(tsibbledata)
library(VIM)
library(Amelia)
library(imputeTS)
library(gridExtra)
library(dygraphs)
library(ggfortify)
library(vars)
library(ggplot2)
library(lubridate)
library(assertthat)
library(xts)
library(MASS)
library(fpp3)
library(GGally)
library(forecast)
library(tseries)2. Conjunto de datos
El conjunto de datos elegido por el grupo se llama “Daily Climate time series data” e incluye información sobre datos diarios climáticos de la ciudad de Delhi en la India en el periodo comprendido entre el 1 de julio de 2013 y el 24 de abril de 2017.
Link del dataset: https://www.kaggle.com/datasets/sumanthvrao/daily-climate-time-series-data?resource=download&select=DailyDelhiClimateTest.csv
2.1. Definición de las variables
Empezando ya el análisis inicial del conjunto de datos que tenemos, vemos que las 5 variables que componen los datos pueden ser descritas como:
Date: fecha en formato YYYY-MM-DD
meantemp: temperatura media calculada en intervalos de tres horas por día
humidity: humedad en el día gramos de vapor de agua por volumen en m3 de aire
wind_speed: velocidad del aire medido en km/h
meanpreassure: presión medida en atm
2.2. Carga de datos
El conjunto de datos “Daily Climate time series data” contiene 5 columnas y 1575 filas (1461 de train y 114 de test) y lo obtenemos en formato .CSV, de dos ficheros diferentes.
Cargamos entonces los datos ya dividos entre train y test.
clima_train <- read.csv("DailyDelhiClimateTrain.csv",sep = ",")
clima_test <- read.csv("DailyDelhiClimateTest.csv",sep = ",")Inicialmente, el conjunto de datos de entrenamiento, se ha guardado un dataframe llamado “clima_train” y se ha realizado un estudio inicial sobre su contenido utilizando la función head y summary.
head(clima_train)## date meantemp humidity wind_speed meanpressure
## 1 2013-01-01 10.000000 84.50000 0.000000 1015.667
## 2 2013-01-02 7.400000 92.00000 2.980000 1017.800
## 3 2013-01-03 7.166667 87.00000 4.633333 1018.667
## 4 2013-01-04 8.666667 71.33333 1.233333 1017.167
## 5 2013-01-05 6.000000 86.83333 3.700000 1016.500
## 6 2013-01-06 7.000000 82.80000 1.480000 1018.000Con la función summary vemos en los estadísticos más importantes de las diferentes variables del dataset y observamos que no existe ningún dato faltante (Na).
summary(clima_train)## date meantemp humidity wind_speed
## Length:1461 Min. : 6.00 Min. :13.43 Min. : 0.000
## Class :character 1st Qu.:18.86 1st Qu.:50.38 1st Qu.: 3.475
## Mode :character Median :27.71 Median :62.62 Median : 6.250
## Mean :25.51 Mean :60.74 Mean : 6.807
## 3rd Qu.:31.31 3rd Qu.:72.12 3rd Qu.: 9.250
## Max. :38.71 Max. :98.00 Max. :42.220
## meanpressure
## Min. : -3.042
## 1st Qu.:1001.571
## Median :1008.556
## Mean :1011.101
## 3rd Qu.:1014.938
## Max. :7679.333Con la función str vemos los diferentes tipos de datos que tenemos en nuestro dataset, y observamos que la variable date está en formato chr.
str(clima_train)## 'data.frame': 1461 obs. of 5 variables:
## $ date : chr "2013-01-01" "2013-01-02" "2013-01-03" "2013-01-04" ...
## $ meantemp : num 10 7.4 7.17 8.67 6 ...
## $ humidity : num 84.5 92 87 71.3 86.8 ...
## $ wind_speed : num 0 2.98 4.63 1.23 3.7 ...
## $ meanpressure: num 1016 1018 1019 1017 1016 ...2.3. Cambio del tipo de variable
Transformamos el formato de la variable date de chr a fecha, tanto en el conjunto de datos de train como en el de test.
clima_train$date<-as.Date(clima_train$date)
str(clima_train)## 'data.frame': 1461 obs. of 5 variables:
## $ date : Date, format: "2013-01-01" "2013-01-02" ...
## $ meantemp : num 10 7.4 7.17 8.67 6 ...
## $ humidity : num 84.5 92 87 71.3 86.8 ...
## $ wind_speed : num 0 2.98 4.63 1.23 3.7 ...
## $ meanpressure: num 1016 1018 1019 1017 1016 ...clima_test$date<-as.Date(clima_test$date)
str(clima_test)## 'data.frame': 114 obs. of 5 variables:
## $ date : Date, format: "2017-01-01" "2017-01-02" ...
## $ meantemp : num 15.9 18.5 17.1 18.7 18.4 ...
## $ humidity : num 85.9 77.2 81.9 70 74.9 ...
## $ wind_speed : num 2.74 2.89 4.02 4.54 3.3 ...
## $ meanpressure: num 59 1018 1018 1016 1014 ...2.4. Definición de los objetivos
El objetivo final del proyecto es conseguir llegar a un modelo de serie temporal que permita realizar una predicción a futuro de la variable temperatura relativa al clima lo más precisa posible.
3. Análisis de la serie temporal
Seleccionamos la variable meantemp relativa a la temperatura media en Delhi, que será la que intentaremos predecir.
temp_train <- clima_train[,c(1,2)]
head(temp_train)## date meantemp
## 1 2013-01-01 10.000000
## 2 2013-01-02 7.400000
## 3 2013-01-03 7.166667
## 4 2013-01-04 8.666667
## 5 2013-01-05 6.000000
## 6 2013-01-06 7.000000Creamos el objeto de serie temporal con la función as_tsibble
temp_train_ts<- as_tsibble(temp_train, index = date)
temp_train_ts## # A tsibble: 1,461 x 2 [1D]
## date meantemp
## <date> <dbl>
## 1 2013-01-01 10
## 2 2013-01-02 7.4
## 3 2013-01-03 7.17
## 4 2013-01-04 8.67
## 5 2013-01-05 6
## 6 2013-01-06 7
## 7 2013-01-07 7
## 8 2013-01-08 8.86
## 9 2013-01-09 14
## 10 2013-01-10 11
## # … with 1,451 more rowsGráfico de la serie temporal de la variable meantemp que queremos anañizar y predecir
temp_train_ts %>%
autoplot(meantemp) +
labs(title = "Temperatura media Delhi 2013-2017") +
xlab("Años") + ylab("Temperatura") 
A simple vista podemos ver cierto componente estacional en las temperaturas que se registran año a año, y una leve tendencia positiva.
3.1. Estacionariedad
Observando el gráfico parece que hay una componente estacional anual, ya que la forma de las series anuales son iguales.
temp_train_ts%>%
gg_season(meantemp, labels = "right")
Calculamos la descomposición STL para observar si existe tendencia y estacionalidad. Gráficamente se puede comprobar que existe estacionalidad y una tendencia creciente.Por tanto, parece que se puede decir que la serie no es estacionaria en media.
temp_train_ts %>%
model(seats = feasts:::STL(meantemp)) %>%
components() %>%
autoplot()
3.1.1. Estacionariedad en Varianza
Ahora estudiamos la estacionariedad en varianza. Dado que obtenemos un valor muy próximo a 1, no realizaremos ningún cambio o transformación Box-Cox para ajustar la varianza y estabilizarla, ya que como podemos observar si se aprecia estacionariedad en varianza.
lambda <- temp_train_ts %>%
features(meantemp, features = guerrero) %>% pull(lambda_guerrero)
lambda## [1] 0.83963613.1.2. Estacionariedad en Media
Comprobamos la estacionariedad en media usando una prueba de raíces unitarias.
temp_train_ts %>%
features(meantemp, unitroot_kpss)## # A tibble: 1 × 2
## kpss_stat kpss_pvalue
## <dbl> <dbl>
## 1 0.589 0.0236El p-valor es menor que 0.05, lo que indica que la hipótesis nula es rechazada. Es decir, los datos no son estacionarios en media. Se confirma formalmente que los datos no son estacionarios.
Para estabilizar la media usamos una diferencia y lo comprobamos con el siguiente test. Obtenemos un p_value mayor de 0.05 por lo que cumpliría la hipótesis de estacionariedad y podemos realizar una diferencia regular para eliminar la tendencia.
temp_train_ts %>%
features(difference(meantemp, 1), unitroot_kpss)## # A tibble: 1 × 2
## kpss_stat kpss_pvalue
## <dbl> <dbl>
## 1 0.128 0.1temp_train_ts %>% autoplot(difference(meantemp, 1)) ## Warning: Removed 1 row(s) containing missing values (geom_path).
Para evaluar si es necesario realizar una diferencia estacional debido a que los datos presentan estacionalidad usaremos unitroot_nsdiffs(). Debido a que es menor a 0.64 el método no sugiere una diferencia estacional.
temp_train_ts %>%
mutate(turnover = difference(meantemp,1)) %>%
features(turnover, unitroot_nsdiffs)## # A tibble: 1 × 1
## nsdiffs
## <int>
## 1 03.2. Creación del modelo (determinación, estimación y contraste)
Creamos las funciones auxiliares que nos servirán para la creación y evaluación del modelo.
# Contraste para los coeficientes
my_t_test <- function (object, ...)
{
par <- rbind(t_stat=tidy(object)$statistic, p_value=tidy(object)$p.value)
colnames(par) <- tidy(object)$term
if (NCOL(par) > 0) {
cat("\nt-test:\n")
coef <- round(par, digits = 4)
print.default(coef, print.gap = 2)
}
}
# Gráfico de correlogramas de residuos
my_tsresiduals <- function (data, ...) {
if (!fabletools::is_mable(data)) {
abort("gg_tsresiduals() must be used with a mable containing only one model.")
}
data <- stats::residuals(data)
if (n_keys(data) > 1) {
abort("gg_tsresiduals() must be used with a mable containing only one model.")
}
gg_tsdisplay(data, !!sym(".resid"), plot_type = "partial",
...)
}
# Validación cruzada anidada
nested_cv <- function(df, h, last_train, string_formula){
nested_errors <- vector()
for (i in seq(last_train, last(df$date), h)){
train <- df %>% filter(date<=i)
test <- df %>% filter(date>i)
fitted_model <- train %>%
model(arima = ARIMA(as.formula(string_formula)))
h_forecast = min(dim(test)[1], h)
fc <- fitted_model %>%
forecast(h=h_forecast)
test_err <- fc %>%
accuracy(test) %>%
select(MAPE)
nested_errors <- c(nested_errors, test_err$MAPE)
NewList <- list("errors"=nested_errors, "mean"=mean(nested_errors))
}
return(NewList)}
# Test de autocorrelacines de los residuos
autocorrelation_test_plot <- function(aug, dof = 4, m = 7, h = 5, alpha = 0.05){
vec <- c()
num_lags = seq(1, h*m)
for (i in num_lags){
vec <- c(vec,aug %>% features(.resid, ljung_box, lag=i, dof=dof) %>% .$lb_pvalue)
}
autocorr_pvalues_resid <- tibble(
lag = num_lags,
p_value = vec,
incorelated = p_value >= alpha
)
plot <- autocorr_pvalues_resid %>%
drop_na() %>%
ggplot(aes(lag, p_value, color = incorelated)) +
geom_point() +
geom_hline(aes(yintercept = alpha), linetype="dashed", color = "indianred2")
newList <- list("values" = autocorr_pvalues_resid, "plot" = plot)
return(newList)
}3.2.1. Creación manual del modelo
En los pasos previos hemos detectado la necesidad de realizar una diferencia regular, pero no una estacional. Por tanto, comenzaremos con el ajuste de un modelo SARIMA (0,1,0)x(0,0,0)[7], sobre la serie.
fit <- temp_train_ts %>%
model(arima = ARIMA(meantemp ~ pdq(0,1,0) + PDQ(0,0,0, period = 7)))
fit %>% my_tsresiduals(lag_max = 36)
Viendo los resultados obtenidos en las gráficas de acf y pacf, empezamos ajustando la serie temporal añadiendo al modelo un 1 en el parámetro “q” relativo a MA en la parte regular de la serie.
fit1 <- temp_train_ts %>%
model(arima = ARIMA(meantemp ~ pdq(0,1,1) + PDQ(0,0,0, period = 7)))
fit1 %>% my_tsresiduals(lag_max = 36)
Añadimos al modelo un 2 en el parámetro “q” relativo a MA en la parte regular de la serie, ya que observamos en las graficas acf/pacf como aún el segundo y tercer lag se salen de las bandas.
fit1 <- temp_train_ts %>%
model(arima = ARIMA(meantemp ~ pdq(0,1,2) + PDQ(0,0,0, period = 7)))
fit1 %>% my_tsresiduals(lag_max = 36)
Añadimos al modelo un 3 en el parámetro “q” relativo a MA en la parte regular de la serie, basándonos en los resultados obtenidos y viendp que el tercer lag en las gráficas de acf/pacf se sigue saliendo de las bandas.
fit1 <- temp_train_ts %>%
model(arima = ARIMA(meantemp ~ pdq(0,1,3) + PDQ(0,0,0, period = 7)))
fit1 %>% my_tsresiduals(lag_max = 36)
Por último añadimos al modelo un 1 en el parámetro “P” relativo a AR en la parte estacional de la serie.
fit1 <- temp_train_ts %>%
model(arima = ARIMA(meantemp ~ pdq(0,1,3) + PDQ(1,0,0, period = 7)))
fit1 %>% my_tsresiduals(lag_max = 36)
Comprobemos la calidad estadística del modelo creado:
report(fit1)## Series: meantemp
## Model: ARIMA(0,1,3)(1,0,0)[7]
##
## Coefficients:
## ma1 ma2 ma3 sar1
## -0.2234 -0.1275 -0.1507 -0.0417
## s.e. 0.0259 0.0269 0.0256 0.0264
##
## sigma^2 estimated as 2.567: log likelihood=-2757.97
## AIC=5525.94 AICc=5525.98 BIC=5552.37my_t_test(fit1)##
## t-test:
## ma1 ma2 ma3 sar1
## t_stat -8.6338 -4.7428 -5.882 -1.5823
## p_value 0.0000 0.0000 0.000 0.1138No es posible identificar más estructura a partir del ACF y PACF, no hay problemas de estacionariedad o invertibilidad. Vemos que todos los parámetros son significativos a excepción de SAR1, cuyo p.value es superior a 0.05. Algunas de las autocorrelaciones se siguen saliendo minimamente de las bandas.
3.2.2. Creación automática del modelo
Utilizamos la función de auto.arima para tratar de obtener un modelo ajustado a nuestra serie temporal generado de forma automática.
#ajuste del modelo automatica
autoarima_model<- auto.arima(temp_train_ts)
autoarima_model## Series: temp_train_ts
## ARIMA(3,1,2)(1,0,0)[7]
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 sar1
## 0.0937 0.2087 -0.0860 -0.3135 -0.3101 -0.0317
## s.e. 0.3635 0.2274 0.0325 0.3646 0.3088 0.0307
##
## sigma^2 = 2.568: log likelihood = -2757.26
## AIC=5528.51 AICc=5528.59 BIC=5565.51El resultado que obtenemos con la función es un SARIMA (3,1,2)x(1,0,0)[7].
fit2 <- temp_train_ts %>%
model(arima = ARIMA(meantemp ~ pdq(3,1,2) + PDQ(1,0,0, period = 7)))
fit2 %>% my_tsresiduals(lag_max = 36)
Vemos como la gráfica ACF/PACF obtenida con el modelo SARIMA (3,1,2)x(1,0,0)[7] que nos arroja la función de auto.arima, es muy similar a la obtenida con el modelo SARIMA (0,1,0)x(0,0,0)[7] sjutado de forma manual.No es posible tampoco identificar más estructura a partir del ACF y PACF.
report(fit2)## Series: meantemp
## Model: ARIMA(3,1,2)(1,0,0)[7]
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 sar1
## 0.0937 0.2087 -0.0860 -0.3135 -0.3101 -0.0317
## s.e. 0.3635 0.2274 0.0325 0.3646 0.3088 0.0307
##
## sigma^2 estimated as 2.568: log likelihood=-2757.26
## AIC=5528.51 AICc=5528.59 BIC=5565.51my_t_test(fit2)##
## t-test:
## ar1 ar2 ar3 ma1 ma2 sar1
## t_stat 0.2578 0.9175 -2.6455 -0.8598 -1.0042 -1.0346
## p_value 0.7966 0.3590 0.0082 0.3900 0.3155 0.3010Vemos que la mayor parte de los parámetros no son significativos a excepción de AR3, cuyo p.value es inferior a 0.05.
3.3. Diagnosis de residuos del modelo final
Finalmente optamos por quedarnos con el modelo ajustado de forma manual: SARIMA (0,1,3)x(1,0,0)[7]
fit4 <- temp_train_ts %>%
model(arima = ARIMA(meantemp ~ pdq(0,1,3) + PDQ(1,0,0, period = 7)))
fit4 %>% my_tsresiduals(lag_max = 36)
TEST NORMALIDAD:
Para completar la fase de contraste del modelo evaluamos sus residuos.
aug <-fit4 %>% augment()
# Histogram
aug %>%
ggplot(aes(x = .resid)) +
geom_histogram(bins = 50) +
ggtitle("Histogram of residuals")
Observando el histograma relativo a los residuos del modelo podemos ver que parece que la media es cero y que sigue medianamente una distribución normal.
Realizamos un test de T-Student para contrastar si realmente la media es cero.
t.test(aug$.resid)##
## One Sample t-test
##
## data: aug$.resid
## t = 0.20445, df = 1460, p-value = 0.838
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.07355211 0.09066786
## sample estimates:
## mean of x
## 0.008557875Como p-value > 0.05 no podemos rechazar la hipótesis de que la muestra tiene media 0.
TEST AUTOCORRELACIONES:
Ahora intentamos comprobar con un test de Ljung-Box que los residuos están incorrelados a través de un test de autocorrelación.
pvals = autocorrelation_test_plot(aug, dof = 4, m = 7, h = 5, alpha = 0.05)## Warning in pchisq(STATISTIC, lag - fitdf): NaNs produced
## Warning in pchisq(STATISTIC, lag - fitdf): NaNs produced
## Warning in pchisq(STATISTIC, lag - fitdf): NaNs producedpvals## $values
## # A tibble: 35 × 3
## lag p_value incorelated
## <int> <dbl> <lgl>
## 1 1 NaN NA
## 2 2 NaN NA
## 3 3 NaN NA
## 4 4 0 FALSE
## 5 5 0.262 TRUE
## 6 6 0.530 TRUE
## 7 7 0.736 TRUE
## 8 8 0.866 TRUE
## 9 9 0.278 TRUE
## 10 10 0.269 TRUE
## # … with 25 more rows
##
## $plot
Los p-valores son mayores de 0.05 en la mayoría de las autocorrelaciones. Por lo tanto, podemos concluir que los residuos no están correlados.
TEST HOMOCEDASTICIDAD:
Utilizamos un regresión media-dispersión para tratar de contrastar la heterocedasticidad (varianza de los errores no es constante). El cálculo de las agrupaciones temporales se realiza de forma anual debido a que esa es la estacionalidad de la serie analizada.
log_log <- aug %>% as_tibble() %>%
group_by(week(date)) %>%
summarize(mean_resid = log(mean(.resid+1)), std_resid = log(sd(.resid+1))) summary(lm(std_resid~mean_resid, log_log))##
## Call:
## lm(formula = std_resid ~ mean_resid, data = log_log)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.76242 -0.15093 0.01077 0.19050 0.55397
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.37742 0.03948 9.560 5.85e-13 ***
## mean_resid -0.01611 0.07267 -0.222 0.825
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2829 on 51 degrees of freedom
## Multiple R-squared: 0.0009632, Adjusted R-squared: -0.01863
## F-statistic: 0.04917 on 1 and 51 DF, p-value: 0.8254Como el p-valor de log(media) es grande, entonces no puede considerarse distinto de 0 y por tanto los residuos son homocedásticos (varianza de los errores es constante).
3.4. Predicción con el modelo final
Antes de nada, unimos los dataset de train y test que teníamos separados para crear uno total de la serie temporal completa.
clima_total<-merge(x=clima_train,y=clima_test,all = TRUE)
head(clima_total)## date meantemp humidity wind_speed meanpressure
## 1 2013-01-01 10.000000 84.50000 0.000000 1015.667
## 2 2013-01-02 7.400000 92.00000 2.980000 1017.800
## 3 2013-01-03 7.166667 87.00000 4.633333 1018.667
## 4 2013-01-04 8.666667 71.33333 1.233333 1017.167
## 5 2013-01-05 6.000000 86.83333 3.700000 1016.500
## 6 2013-01-06 7.000000 82.80000 1.480000 1018.000El dataset creado con los datos totales lo pasamos a tsibble
temp_total <- clima_total[,c(1,2)]
head(temp_total)## date meantemp
## 1 2013-01-01 10.000000
## 2 2013-01-02 7.400000
## 3 2013-01-03 7.166667
## 4 2013-01-04 8.666667
## 5 2013-01-05 6.000000
## 6 2013-01-06 7.000000temp_total_ts<- as_tsibble(temp_total, index = date)
temp_total_ts## # A tsibble: 1,575 x 2 [1D]
## date meantemp
## <date> <dbl>
## 1 2013-01-01 10
## 2 2013-01-02 7.4
## 3 2013-01-03 7.17
## 4 2013-01-04 8.67
## 5 2013-01-05 6
## 6 2013-01-06 7
## 7 2013-01-07 7
## 8 2013-01-08 8.86
## 9 2013-01-09 14
## 10 2013-01-10 11
## # … with 1,565 more rowsComenzamos a realizar la predicción con el modelo final y a evaluar su capacidad predictiva. Calculamos las predicciones en el conjunto de test, calculamos sus errores y los comparamos con los residuos.
# Residual accuracy
resids <- fit4 %>%
accuracy() %>%
dplyr::select(-c(.model, .type, ME, MPE, ACF1, RMSSE)) %>%
mutate(Evaluation='Training')
# Forecasting
fc <- fit4 %>%
forecast(h=7)
test_err <- fc %>%
accuracy(temp_total_ts) %>%
dplyr::select(-c(.model, .type, ME, MPE, ACF1, RMSSE)) %>%
mutate(Evaluation='Test')
# Show errors together
bind_rows(test_err, resids) %>% dplyr::select(Evaluation, everything())## # A tibble: 2 × 5
## Evaluation RMSE MAE MAPE MASE
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 Test 2.50 2.21 12.2 0.944
## 2 Training 1.60 1.21 5.26 0.518Tratamos de evaluar también año a año la serie temporal real con la predicha para evaluar así los errores, detectar atípicos y analizar efectos de calendario sobre la misma.
aug %>% ggplot() +
geom_line(aes(x = date, y = .fitted), color="navy") +
geom_line(aes(x = date, y = meantemp), color="gray24") +
# geom_line(data=demandaGas_forecast, aes(x = index, y = value), color="red4") +
ggtitle("SARIMA train fitted values") +
xlab('Dates') +
ylab('meantemp') + facet_wrap(vars(year(date)), scales = 'free')
aug %>% filter(year(date) == 2013) %>%
ggplot() +
geom_line(aes(x = date, y = .fitted), color="navy") +
geom_line(aes(x = date, y = meantemp), color="gray24") +
# geom_line(data=demandaGas_forecast, aes(x = index, y = value), color="red4") +
ggtitle("SARIMA train fitted values") +
xlab('Dates') +
ylab('meantemp') + facet_wrap(vars(month(date)), scales = 'free')
Vemos en los gráficos mensuales mostrados como hay un problema en la predicción de la serie, mostrando un cierto retardo en la estimación de los valores.
Para finalmente tratar de ver la capacidad predictora del modelo, transformamos el dataset con los datos de test a tsibble.
temp_test <- clima_test[,c(1,2)]
head(temp_train)## date meantemp
## 1 2013-01-01 10.000000
## 2 2013-01-02 7.400000
## 3 2013-01-03 7.166667
## 4 2013-01-04 8.666667
## 5 2013-01-05 6.000000
## 6 2013-01-06 7.000000temp_test_ts<- as_tsibble(temp_test, index = date)
temp_test_ts## # A tsibble: 114 x 2 [1D]
## date meantemp
## <date> <dbl>
## 1 2017-01-01 15.9
## 2 2017-01-02 18.5
## 3 2017-01-03 17.1
## 4 2017-01-04 18.7
## 5 2017-01-05 18.4
## 6 2017-01-06 19.3
## 7 2017-01-07 14.7
## 8 2017-01-08 15.7
## 9 2017-01-09 14.6
## 10 2017-01-10 12.1
## # … with 104 more rowsAnalizamos la capacidad predictora del modelo y sus intervalos de confianza.
h <- dim(temp_test_ts)[1]
demanda_plot <- temp_total_ts %>% filter(date>last(temp_train_ts$date)-14 & date< last(temp_train_ts$date) + 7 )
fit4 %>%
forecast(h=7) %>%
autoplot(demanda_plot)
Vemos que la capacidad predictora de nuestro modelo es mala en el periodo de 7 días analizado. Tenemos una serie con multiestacionalidad y un modelo que no está siendo capaz de captarla y representarla, por lo que las predicciones que obtenemos no son las deseadas. Deberíamos tratar de utilizar técnicas y modelos más complejos que traten de ajustarse de mejor forma a las características de nuestra serie.
4. Modelo de Naive Bayes estacional
Para tratar de comparar el modelo SARIMA creado con alguna alternativa que nos permita realizar una mejor predicción, desarrollamos un modelo Naive Bayes estacional para nuestra serie.
Inicialmente convertimos los datos de nuestra serie temporal estacional a TS.
ts_train_ts <- ts(temp_train$meantemp, start = c(2013,1), frequency=365)
head(ts_train_ts)## Time Series:
## Start = c(2013, 1)
## End = c(2013, 6)
## Frequency = 365
## [1] 10.000000 7.400000 7.166667 8.666667 6.000000 7.000000A través de la función Window cogemos la venta temporal sobre la que queremos realizar la predicción con el modelo de Bayes.
ts_naive <- window(ts_train_ts,start=c(2013,1),end=c(2017,1))
autoplot(ts_naive) 
Con la función SNAIVE y los datos de la serie ya transformados a TS, creamos el modelo de Naive Bayes estacional para realizar la predicción de los datos.
ts_naive_forecast <- snaive(ts_naive ,h=114)
head(ts_naive_forecast)## $method
## [1] "Seasonal naive method"
##
## $model
## Call: snaive(y = ts_naive, h = 114)
##
## Residual sd: 3.2301
##
## $lambda
## NULL
##
## $x
## Time Series:
## Start = c(2013, 1)
## End = c(2017, 1)
## Frequency = 365
## [1] 10.000000 7.400000 7.166667 8.666667 6.000000 7.000000 7.000000
## [8] 8.857143 14.000000 11.000000 15.714286 14.000000 15.833333 12.833333
## [15] 14.714286 13.833333 16.500000 13.833333 12.500000 11.285714 11.200000
## [22] 9.500000 14.000000 13.833333 12.250000 12.666667 12.857143 14.833333
## [29] 14.125000 14.714286 16.200000 16.000000 16.285714 18.000000 17.428571
## [36] 16.625000 16.666667 15.600000 14.000000 15.428571 15.250000 15.875000
## [43] 15.333333 16.285714 17.333333 19.166667 14.428571 13.666667 15.600000
## [50] 15.857143 17.714286 20.000000 20.500000 17.428571 16.857143 16.875000
## [57] 17.857143 20.800000 19.428571 17.333333 19.000000 19.333333 17.600000
## [64] 20.875000 20.857143 23.428571 24.166667 25.428571 23.142857 24.000000
## [71] 23.500000 21.500000 22.333333 24.166667 20.333333 22.666667 23.428571
## [78] 22.500000 29.166667 23.833333 25.250000 27.375000 27.000000 23.500000
## [85] 24.142857 21.000000 22.428571 21.250000 23.500000 23.200000 25.375000
## [92] 25.166667 26.200000 24.600000 25.600000 25.857143 29.142857 28.714286
## [99] 30.166667 30.000000 30.000000 28.857143 30.200000 28.250000 28.250000
## [106] 32.125000 29.200000 30.285714 28.285714 30.625000 27.666667 27.375000
## [113] 28.625000 30.285714 31.142857 29.875000 31.142857 30.571429 32.125000
## [120] 31.142857 31.857143 29.833333 28.571429 32.857143 32.625000 32.750000
## [127] 32.875000 34.500000 34.285714 34.000000 30.750000 29.857143 31.714286
## [134] 32.285714 33.000000 33.000000 32.833333 31.400000 35.333333 36.400000
## [141] 36.000000 36.750000 37.500000 38.428571 38.714286 37.800000 35.857143
## [148] 35.333333 34.142857 32.200000 33.625000 32.000000 32.400000 35.600000
## [155] 35.857143 37.166667 31.285714 34.000000 34.200000 36.166667 36.625000
## [162] 30.166667 34.142857 29.833333 30.142857 30.714286 27.000000 26.875000
## [169] 28.400000 29.857143 33.000000 34.833333 35.600000 35.166667 33.142857
## [176] 30.571429 30.666667 31.428571 31.500000 33.250000 32.833333 33.857143
## [183] 33.142857 31.571429 32.375000 32.800000 31.000000 31.166667 29.833333
## [190] 29.000000 29.750000 32.500000 28.875000 31.750000 30.750000 31.750000
## [197] 29.875000 31.125000 31.750000 30.500000 26.833333 28.200000 29.500000
## [204] 31.857143 29.714286 28.333333 30.000000 30.142857 32.285714 31.000000
## [211] 30.500000 28.833333 30.000000 31.571429 32.500000 32.500000 29.500000
## [218] 27.166667 28.375000 28.500000 27.166667 29.428571 30.000000 29.500000
## [225] 30.750000 29.666667 27.714286 26.600000 27.428571 28.333333 28.166667
## [232] 27.375000 28.333333 29.166667 31.285714 32.000000 29.000000 32.000000
## [239] 32.142857 30.142857 31.500000 29.166667 29.000000 30.000000 31.857143
## [246] 32.750000 31.714286 31.666667 30.571429 30.833333 28.000000 31.000000
## [253] 29.666667 30.857143 31.166667 31.142857 30.500000 31.625000 29.666667
## [260] 29.250000 29.142857 29.800000 28.666667 25.200000 28.333333 30.285714
## [267] 30.750000 28.571429 28.200000 29.000000 30.000000 28.142857 26.857143
## [274] 28.285714 29.200000 28.600000 24.833333 28.500000 29.750000 29.714286
## [281] 29.200000 30.833333 29.428571 23.857143 26.142857 27.166667 27.714286
## [288] 25.857143 26.428571 26.857143 26.333333 24.571429 24.333333 24.875000
## [295] 27.800000 25.000000 23.857143 22.800000 23.000000 22.875000 22.666667
## [302] 23.000000 22.857143 23.666667 23.428571 21.625000 20.625000 21.166667
## [309] 18.833333 20.571429 20.142857 18.000000 19.857143 16.833333 18.857143
## [316] 16.571429 17.750000 17.625000 17.000000 16.625000 15.571429 18.500000
## [323] 17.875000 18.250000 17.875000 17.625000 18.142857 19.125000 21.250000
## [330] 21.250000 19.125000 18.625000 17.750000 17.875000 18.000000 17.250000
## [337] 17.500000 17.142857 17.142857 16.125000 16.000000 16.500000 16.125000
## [344] 15.500000 16.625000 17.750000 17.142857 16.142857 15.500000 15.250000
## [351] 14.750000 14.875000 16.125000 15.375000 14.750000 15.250000 14.250000
## [358] 13.500000 13.666667 12.125000 11.875000 10.875000 10.571429 12.375000
## [365] 14.500000 13.375000 11.000000 12.500000 12.875000 12.375000 11.428571
## [372] 12.142857 11.875000 12.833333 12.375000 12.125000 12.875000 14.000000
## [379] 14.875000 12.000000 12.285714 12.000000 12.500000 14.500000 14.625000
## [386] 13.571429 15.250000 15.625000 13.875000 11.750000 14.375000 16.625000
## [393] 16.625000 14.875000 14.500000 14.750000 14.000000 15.250000 18.428571
## [400] 18.857143 17.000000 18.500000 19.625000 13.625000 12.875000 12.625000
## [407] 13.375000 13.250000 15.250000 13.000000 12.375000 13.500000 15.125000
## [414] 15.250000 15.125000 16.125000 17.125000 16.625000 16.500000 16.375000
## [421] 18.125000 18.750000 18.625000 15.625000 16.142857 16.125000 17.875000
## [428] 18.750000 18.875000 18.375000 18.500000 19.875000 22.000000 20.000000
## [435] 20.714286 20.000000 19.000000 19.625000 21.625000 23.125000 26.250000
## [442] 24.857143 21.750000 21.500000 22.500000 25.000000 22.750000 22.375000
## [449] 24.625000 25.125000 23.500000 24.428571 25.875000 24.125000 24.125000
## [456] 24.875000 26.750000 25.000000 25.857143 27.375000 30.125000 27.250000
## [463] 25.750000 25.750000 26.375000 28.142857 29.125000 26.875000 27.625000
## [470] 29.000000 27.125000 26.375000 24.250000 25.625000 27.000000 28.000000
## [477] 29.375000 29.125000 29.375000 30.625000 31.500000 30.625000 31.500000
## [484] 32.125000 33.250000 34.875000 34.375000 31.750000 31.875000 29.750000
## [491] 29.571429 31.750000 31.375000 30.500000 30.000000 29.625000 28.000000
## [498] 25.250000 26.875000 29.500000 31.125000 29.875000 31.500000 32.375000
## [505] 31.125000 33.000000 33.250000 34.625000 31.500000 31.500000 30.125000
## [512] 31.875000 33.625000 35.250000 33.125000 34.625000 32.750000 32.750000
## [519] 34.875000 35.250000 36.875000 37.500000 38.500000 37.625000 37.875000
## [526] 37.250000 37.625000 32.875000 30.250000 30.500000 33.875000 36.375000
## [533] 36.875000 33.875000 35.750000 38.000000 36.875000 34.500000 32.125000
## [540] 33.000000 32.250000 32.500000 34.750000 34.875000 33.000000 32.000000
## [547] 31.375000 29.500000 28.875000 31.388889 34.705882 30.625000 34.000000
## [554] 35.000000 36.000000 36.125000 36.625000 35.875000 31.625000 32.375000
## [561] 33.125000 32.625000 30.750000 27.250000 29.875000 30.875000 32.125000
## [568] 31.625000 30.625000 30.500000 30.750000 32.500000 31.714286 30.000000
## [575] 30.250000 31.875000 32.500000 33.250000 30.125000 31.500000 30.500000
## [582] 29.750000 32.125000 31.125000 31.000000 29.235294 28.500000 31.125000
## [589] 32.125000 32.125000 30.375000 31.125000 30.428571 31.375000 31.875000
## [596] 33.000000 33.250000 32.500000 33.000000 33.125000 33.125000 33.875000
## [603] 34.125000 33.857143 29.625000 30.375000 28.625000 27.625000 29.428571
## [610] 29.250000 28.625000 27.875000 26.500000 28.500000 31.000000 31.250000
## [617] 31.000000 28.750000 26.571429 28.500000 29.375000 29.125000 29.625000
## [624] 30.625000 30.625000 30.500000 31.000000 31.125000 30.500000 30.625000
## [631] 31.000000 29.625000 30.000000 30.000000 30.500000 30.250000 30.500000
## [638] 30.625000 30.428571 30.375000 30.500000 31.000000 30.625000 30.625000
## [645] 31.000000 28.750000 27.625000 27.125000 25.714286 26.000000 27.625000
## [652] 24.500000 24.500000 23.000000 25.000000 24.000000 23.750000 24.750000
## [659] 25.625000 25.750000 25.250000 25.500000 25.250000 25.125000 24.875000
## [666] 25.125000 24.750000 23.875000 23.375000 22.500000 22.875000 23.375000
## [673] 23.625000 22.750000 23.000000 24.000000 23.875000 24.125000 21.375000
## [680] 19.250000 19.625000 18.500000 18.375000 18.625000 18.250000 17.750000
## [687] 17.625000 17.500000 20.375000 18.250000 19.875000 17.125000 16.875000
## [694] 16.500000 19.625000 18.125000 19.375000 20.250000 19.750000 20.000000
## [701] 21.375000 25.000000 21.250000 17.750000 18.250000 17.250000 17.000000
## [708] 15.285714 21.500000 19.625000 17.500000 16.000000 16.875000 16.625000
## [715] 17.750000 12.875000 11.750000 11.750000 11.250000 9.500000 9.375000
## [722] 9.625000 9.875000 9.250000 10.750000 10.375000 9.000000 11.125000
## [729] 11.625000 12.375000 14.750000 14.875000 15.125000 14.125000 14.000000
## [736] 12.000000 9.625000 10.000000 10.625000 11.125000 11.000000 10.625000
## [743] 12.250000 12.000000 12.375000 13.000000 13.500000 13.000000 13.750000
## [750] 13.375000 13.250000 12.625000 14.625000 12.375000 13.250000 13.750000
## [757] 13.250000 11.714286 11.500000 12.750000 13.750000 15.000000 17.375000
## [764] 16.750000 14.625000 14.625000 15.125000 15.875000 16.625000 16.875000
## [771] 15.750000 16.000000 15.500000 17.250000 19.375000 18.875000 20.625000
## [778] 21.142857 21.250000 22.750000 22.750000 21.875000 22.142857 21.500000
## [785] 22.875000 23.125000 20.000000 19.250000 21.250000 17.375000 17.500000
## [792] 16.250000 16.750000 18.750000 20.000000 18.375000 19.500000 18.125000
## [799] 17.750000 18.250000 20.500000 21.375000 21.500000 17.625000 19.857143
## [806] 20.875000 20.250000 21.125000 22.500000 24.875000 25.125000 24.750000
## [813] 25.750000 26.625000 28.500000 27.375000 27.000000 25.000000 23.500000
## [820] 25.250000 26.428571 28.714286 24.500000 21.000000 23.571429 25.000000
## [827] 23.750000 25.625000 26.000000 27.125000 28.250000 24.375000 24.750000
## [834] 26.250000 27.625000 25.250000 28.125000 30.125000 32.125000 32.875000
## [841] 31.750000 30.750000 30.750000 31.125000 30.500000 28.750000 30.125000
## [848] 31.000000 31.250000 32.625000 31.250000 30.125000 31.000000 30.875000
## [855] 32.125000 34.125000 35.428571 34.125000 35.125000 35.125000 34.000000
## [862] 33.125000 27.750000 29.625000 28.500000 30.000000 33.250000 35.375000
## [869] 31.500000 33.125000 35.625000 36.250000 37.375000 36.000000 37.750000
## [876] 35.250000 33.750000 34.750000 35.125000 32.250000 34.250000 29.375000
## [883] 31.625000 28.625000 31.875000 32.625000 33.375000 35.000000 36.500000
## [890] 37.625000 36.625000 35.625000 35.875000 31.125000 27.000000 31.000000
## [897] 32.375000 33.875000 35.125000 35.875000 33.125000 30.375000 32.125000
## [904] 31.500000 37.250000 26.625000 31.125000 32.625000 34.250000 31.125000
## [911] 30.875000 32.000000 33.750000 33.000000 34.125000 35.714286 27.875000
## [918] 28.125000 31.250000 29.625000 26.625000 25.500000 25.500000 29.875000
## [925] 30.875000 33.375000 31.750000 30.750000 29.500000 30.125000 29.125000
## [932] 31.375000 32.250000 32.125000 32.000000 30.857143 30.000000 29.625000
## [939] 29.500000 28.500000 29.000000 29.000000 28.250000 29.625000 31.500000
## [946] 29.428571 29.593750 29.500000 29.250000 28.875000 27.375000 30.375000
## [953] 28.375000 30.750000 32.000000 30.875000 28.500000 28.625000 30.750000
## [960] 29.125000 31.250000 30.750000 29.375000 30.250000 29.875000 30.750000
## [967] 32.000000 32.000000 32.500000 32.000000 32.250000 32.625000 31.857143
## [974] 32.125000 31.875000 31.625000 32.000000 30.875000 31.250000 31.500000
## [981] 31.625000 31.000000 31.250000 30.750000 32.142857 32.125000 31.875000
## [988] 33.000000 32.375000 31.375000 31.000000 30.625000 29.142857 30.125000
## [995] 30.250000 28.625000 28.250000 28.500000 29.250000 28.714286 28.250000
## [1002] 29.000000 29.000000 28.125000 28.285714 30.000000 29.000000 28.875000
## [1009] 28.375000 28.625000 28.375000 28.500000 28.500000 28.571429 29.250000
## [1016] 29.500000 28.125000 27.500000 27.875000 28.000000 26.857143 28.142857
## [1023] 27.714286 26.500000 24.750000 24.000000 24.875000 26.375000 25.625000
## [1030] 24.750000 20.875000 22.125000 22.375000 22.375000 22.875000 23.375000
## [1037] 24.000000 23.750000 22.125000 22.875000 21.875000 21.875000 21.750000
## [1044] 22.750000 21.875000 21.875000 22.375000 22.375000 22.500000 21.875000
## [1051] 19.875000 18.500000 18.500000 18.500000 18.750000 18.625000 17.000000
## [1058] 18.500000 19.375000 20.000000 18.500000 18.750000 18.125000 19.500000
## [1065] 19.250000 18.125000 17.625000 17.625000 17.500000 17.125000 17.625000
## [1072] 18.428571 18.375000 19.000000 17.250000 13.250000 12.875000 13.250000
## [1079] 13.125000 13.000000 12.250000 12.875000 12.375000 11.750000 12.625000
## [1086] 12.000000 12.500000 11.250000 11.500000 12.750000 15.375000 17.125000
## [1093] 16.375000 15.500000 15.000000 14.714286 14.000000 14.375000 15.750000
## [1100] 15.833333 17.375000 17.125000 15.500000 15.857143 15.625000 15.750000
## [1107] 18.000000 18.266667 15.562500 13.000000 13.600000 14.000000 13.266667
## [1114] 12.357143 12.066667 12.187500 11.733333 14.437500 11.187500 11.666667
## [1121] 14.562500 17.583333 16.857143 19.562500 20.142857 17.375000 15.846154
## [1128] 15.266667 13.125000 16.363636 12.666667 15.333333 15.625000 17.090909
## [1135] 17.769231 18.133333 19.687500 19.200000 17.066667 17.642857 17.600000
## [1142] 18.214286 18.714286 19.466667 23.153846 23.625000 21.000000 21.000000
## [1149] 21.428571 21.687500 22.562500 22.800000 22.800000 23.000000 23.875000
## [1156] 24.916667 24.933333 26.000000 27.312500 23.933333 22.812500 23.714286
## [1163] 23.428571 24.000000 25.562500 25.066667 24.562500 24.250000 22.375000
## [1170] 24.066667 23.937500 26.312500 26.187500 26.785714 27.133333 26.625000
## [1177] 25.062500 26.200000 28.133333 29.875000 24.666667 26.250000 25.933333
## [1184] 27.125000 29.571429 30.000000 30.571429 32.312500 33.312500 32.812500
## [1191] 32.312500 31.375000 29.933333 29.266667 30.733333 32.250000 29.800000
## [1198] 30.200000 31.750000 33.125000 33.625000 35.687500 34.666667 34.625000
## [1205] 34.000000 34.062500 34.000000 33.250000 31.916667 31.312500 31.750000
## [1212] 33.437500 33.125000 34.153846 34.071429 33.062500 34.687500 38.000000
## [1219] 35.500000 33.714286 30.600000 31.437500 33.312500 35.133333 33.533333
## [1226] 34.000000 32.500000 35.375000 37.294118 36.562500 37.250000 37.214286
## [1233] 37.500000 37.750000 37.375000 37.400000 36.133333 36.800000 32.214286
## [1240] 31.526316 33.217391 35.269231 38.272727 36.062500 31.500000 26.812500
## [1247] 32.642857 36.000000 37.562500 37.562500 38.200000 36.166667 35.428571
## [1254] 34.625000 36.071429 35.733333 36.133333 33.437500 35.500000 36.000000
## [1261] 32.625000 34.733333 33.500000 34.187500 35.857143 35.625000 30.937500
## [1268] 32.875000 33.125000 33.846154 36.437500 35.428571 34.866667 34.312500
## [1275] 30.785714 35.375000 35.466667 32.125000 28.400000 29.562500 30.687500
## [1282] 33.250000 33.266667 33.500000 30.800000 33.250000 32.562500 31.500000
## [1289] 30.500000 31.250000 30.437500 31.000000 27.125000 28.125000 27.666667
## [1296] 32.312500 34.187500 34.133333 34.125000 31.875000 31.437500 31.937500
## [1303] 30.312500 28.312500 29.533333 27.375000 27.333333 29.266667 29.125000
## [1310] 30.687500 32.562500 33.111111 33.800000 30.066667 33.117647 33.809524
## [1317] 31.615385 32.000000 28.107143 29.035714 30.321429 28.933333 31.678571
## [1324] 31.333333 29.928571 29.888889 32.071429 33.185185 31.592593 32.185185
## [1331] 31.480000 30.178571 31.520000 31.222222 31.785714 33.400000 29.571429
## [1338] 30.040000 27.259259 27.960000 30.739130 30.894737 31.692308 31.076923
## [1345] 30.375000 31.100000 31.916667 30.555556 31.230769 31.000000 31.642857
## [1352] 32.533333 30.857143 31.727273 31.400000 32.307692 32.250000 32.375000
## [1359] 33.444444 33.360000 30.037037 31.000000 31.240000 31.130435 31.480000
## [1366] 32.185185 32.440000 32.227273 32.214286 32.541667 32.814815 33.269231
## [1373] 30.555556 28.833333 30.703704 30.960000 30.600000 30.920000 29.777778
## [1380] 29.666667 29.571429 29.962963 29.750000 27.740741 28.428571 28.600000
## [1387] 28.500000 28.925926 29.076923 28.409091 29.333333 27.500000 28.500000
## [1394] 28.040000 27.576923 26.555556 25.518519 25.814815 24.826087 24.538462
## [1401] 24.384615 23.727273 25.640000 24.814815 23.115385 22.925926 24.545455
## [1408] 23.730769 23.000000 23.518519 23.920000 23.538462 24.296296 23.346154
## [1415] 22.240000 21.769231 21.730769 21.730769 20.666667 22.250000 21.538462
## [1422] 22.578947 22.826087 21.421053 23.600000 24.294118 23.636364 22.454545
## [1429] 21.611111 19.869565 19.750000 19.208333 21.208333 18.900000 18.636364
## [1436] 18.538462 18.250000 16.900000 19.416667 16.444444 20.041667 19.909091
## [1443] 19.050000 18.555556 18.166667 15.833333 17.500000 16.083333 17.857143
## [1450] 19.800000 18.050000 17.285714 15.550000 17.318182 14.000000 17.142857
## [1457] 16.850000 17.217391 15.238095 14.095238 15.052632
##
## $fitted
## Time Series:
## Start = c(2013, 1)
## End = c(2017, 1)
## Frequency = 365
## [1] NA NA NA NA NA NA NA
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## [645] 29.714286 29.200000 30.833333 29.428571 23.857143 26.142857 27.166667
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## [1380] 29.250000 29.500000 28.125000 27.500000 27.875000 28.000000 26.857143
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## [1394] 25.625000 24.750000 20.875000 22.125000 22.375000 22.375000 22.875000
## [1401] 23.375000 24.000000 23.750000 22.125000 22.875000 21.875000 21.875000
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## [1436] 17.625000 18.428571 18.375000 19.000000 17.250000 13.250000 12.875000
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## [1457] 17.125000 16.375000 15.500000 15.000000 14.714286
##
## $residuals
## Time Series:
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## End = c(2017, 1)
## Frequency = 365
## [1] NA NA NA NA NA
## [6] NA NA NA NA NA
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## [26] NA NA NA NA NA
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## [36] NA NA NA NA NA
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## [271] NA NA NA NA NA
## [276] NA NA NA NA NA
## [281] NA NA NA NA NA
## [286] NA NA NA NA NA
## [291] NA NA NA NA NA
## [296] NA NA NA NA NA
## [301] NA NA NA NA NA
## [306] NA NA NA NA NA
## [311] NA NA NA NA NA
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## [331] NA NA NA NA NA
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## [341] NA NA NA NA NA
## [346] NA NA NA NA NA
## [351] NA NA NA NA NA
## [356] NA NA NA NA NA
## [361] NA NA NA NA NA
## [366] 3.375000000 3.600000000 5.333333333 4.208333333 6.375000000
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## [386] 2.371428571 5.750000000 1.625000000 0.041666667 -0.500000000
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## [446] -0.250000000 -4.625000000 -4.625000000 1.125000000 0.982142857
## [451] 2.500000000 2.000000000 4.625000000 0.625000000 0.925000000
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## [986] 2.750000000 2.750000000 3.375000000 1.750000000 0.750000000
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## [1021] 2.857142857 4.392857143 2.964285714 0.875000000 -1.000000000
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## [1101] 5.375000000 7.500000000 5.500000000 5.232142857 4.500000000
## [1106] 4.750000000 7.375000000 6.016666667 3.562500000 0.625000000
## [1111] 0.600000000 0.500000000 0.266666667 -1.392857143 -1.308333333
## [1116] -1.062500000 -0.891666667 -0.187500000 -1.187500000 -1.583333333
## [1121] 0.812500000 4.333333333 5.142857143 8.062500000 7.392857143
## [1126] 3.625000000 0.846153846 -2.108333333 -3.625000000 1.738636364
## [1131] -1.958333333 0.208333333 -0.250000000 0.465909091 0.894230769
## [1136] 2.383333333 3.687500000 3.700000000 -0.183333333 -1.732142857
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## [1156] 7.416666667 8.683333333 9.250000000 8.562500000 3.933333333
## [1161] 4.437500000 4.214285714 5.303571429 6.250000000 7.312500000
## [1166] 4.566666667 3.187500000 2.750000000 4.750000000 4.209523810
## [1171] 3.062500000 6.062500000 5.062500000 4.285714286 2.258333333
## [1176] 1.500000000 0.312500000 0.450000000 1.508333333 1.375000000
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## [1186] 3.571428571 1.857142857 7.812500000 12.312500000 9.241071429
## [1191] 7.312500000 7.625000000 4.308333333 3.266666667 3.608333333
## [1196] 4.000000000 5.425000000 5.450000000 5.500000000 5.500000000
## [1201] 8.375000000 7.562500000 4.541666667 2.500000000 1.125000000
## [1206] 2.312500000 3.250000000 2.500000000 0.791666667 0.812500000
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## [1216] 1.812500000 4.562500000 7.000000000 4.625000000 1.589285714
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## [1226] 0.000000000 -0.625000000 7.625000000 7.669117647 8.062500000
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## [1256] -0.891666667 0.508333333 -2.437500000 4.375000000 9.000000000
## [1261] 1.625000000 2.358333333 -0.375000000 -0.937500000 -0.017857143
## [1266] 2.500000000 0.562500000 0.750000000 1.625000000 -3.403846154
## [1271] 9.812500000 4.303571429 2.241666667 0.062500000 -0.339285714
## [1276] 4.500000000 3.466666667 -1.625000000 -4.600000000 -4.562500000
## [1281] -5.026785714 5.375000000 5.141666667 2.250000000 1.175000000
## [1286] 6.625000000 7.062500000 6.000000000 0.625000000 0.375000000
## [1291] -2.937500000 -0.750000000 -3.625000000 -1.375000000 -2.458333333
## [1296] 3.187500000 2.812500000 1.883333333 2.000000000 -0.125000000
## [1301] 0.580357143 1.937500000 0.687500000 -1.187500000 1.033333333
## [1306] -1.625000000 -1.666666667 1.016666667 -0.500000000 -0.812500000
## [1311] 3.133928571 3.517361111 4.300000000 0.816666667 4.242647059
## [1316] 6.434523810 1.240384615 3.625000000 -2.642857143 -2.964285714
## [1321] -0.553571429 0.433333333 3.053571429 0.583333333 0.803571429
## [1326] -1.361111111 1.321428571 3.810185185 1.342592593 2.310185185
## [1331] 0.730000000 -1.821428571 -0.480000000 -1.277777778 -0.214285714
## [1336] 1.150000000 -3.053571429 -1.817142857 -4.865740741 -3.915000000
## [1341] -0.885869565 -1.105263158 0.817307692 -0.173076923 -1.125000000
## [1346] -0.525000000 0.916666667 -0.694444444 0.480769231 -1.142857143
## [1351] -0.482142857 0.658333333 -2.142857143 -0.647727273 0.025000000
## [1356] 1.307692308 1.625000000 3.232142857 3.319444444 3.110000000
## [1361] 1.412037037 2.750000000 2.740000000 1.880434783 2.765714286
## [1366] 3.935185185 3.440000000 3.227272727 4.089285714 4.255952381
## [1371] 2.814814815 4.269230769 1.680555556 0.458333333 2.078703704
## [1376] 2.585000000 2.100000000 2.420000000 1.206349206 0.416666667
## [1381] 0.071428571 1.837962963 2.250000000 -0.134259259 0.428571429
## [1386] 1.742857143 0.357142857 1.211640212 2.576923077 3.659090909
## [1391] 5.333333333 2.625000000 2.125000000 2.415000000 2.826923077
## [1396] 5.680555556 3.393518519 3.439814815 2.451086957 1.663461538
## [1401] 1.009615385 -0.272727273 1.890000000 2.689814815 0.240384615
## [1406] 1.050925926 2.670454545 1.980769231 0.250000000 1.643518519
## [1411] 2.045000000 1.163461538 1.921296296 0.846153846 0.365000000
## [1416] 1.894230769 3.230769231 3.230769231 2.166666667 3.500000000
## [1421] 2.913461538 5.578947368 4.326086957 2.046052632 3.600000000
## [1426] 5.794117647 4.886363636 4.329545455 2.111111111 0.619565217
## [1431] 1.625000000 1.583333333 3.583333333 1.400000000 1.511363636
## [1436] 0.913461538 -0.178571429 -1.475000000 0.416666667 -0.805555556
## [1441] 6.791666667 7.034090909 5.800000000 5.430555556 5.166666667
## [1446] 3.583333333 4.625000000 3.708333333 6.107142857 7.175000000
## [1451] 6.050000000 4.785714286 4.300000000 5.818181818 1.250000000
## [1456] 1.767857143 -0.275000000 0.842391304 -0.261904762 -0.904761905
## [1461] 0.338345865plot(ts_naive_forecast)
ts_total_ts <- ts(temp_total$meantemp, start = c(2013,1), frequency=365)
head(ts_total_ts)## Time Series:
## Start = c(2013, 1)
## End = c(2013, 6)
## Frequency = 365
## [1] 10.000000 7.400000 7.166667 8.666667 6.000000 7.000000autoplot(ts_total_ts) 
Vemos que la predicción realizada con el modelo de Naive Bayes es más precisa en este caso que la realizada con SARIMA, obteniendo un forecast con los datos de test cercano a los datos reales.